In the genteel south, these aren't roaches, they're water bugs. Roaches are much smaller and prone to infestation. These big old guys can fly and you only see one every couple of months. It's horrible, but infrequent. And you almost always find them dead. Feet up.

Once again, for clarity, this is a picture from a google of the word "dead roach." NOT FROM MY HOME. :)

Phew. For a moment there, I thought you'd snuck into my old apartment and photographed the three amigos. They're rather sad little things, aren't they? I mean, to die with your legs -- all of them -- in the air... so humiliating. Yuck.

Yes unfortunately water bugs and roaches are one in the same. the palemetto bug is also known as the American Cockroach. The reason why they die on their back is because of the unablity to flip back over. They aren't able to get to food or water. also they landed on their backs because they fell off of something.